Phi (φ), golden section, golden mean, extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, golden number, or mean of Phidias are the other names for the "Golden Ratio".
The Golden Ratio:
The golden ratio is the number often encountered when taking the ratios of distances in simple geometric figures, like pentagon, pentagram, decagon, and dodecahedron. If the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller quantity, then those to quantities are in the golden ratio. The golden ratio is approximately 1.6180339887... , which is similar to pi (π) because they are both irrational mathematical constant. The golden ratio can be found in almost everywhere, as in architecture, painting, book design, music, nature, mathematics, etc.
History of the Golden Ratio:
The study of the golden ratio started at least 2400 years ago by ancient Greek mathematicians because of its frequent appearance in geometry. In Elements, Euclid's book that was one of the first and influential book of golden ratio, he defined the golden ratio as: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser" Luca Pacioli, who captured golden ratio in the imaginations of artist, architects, scientist, and mystics, started the modern history of the golden ratio. It was twentieth century when the golden ratio started to be commonly represented by the Greek letter φ (phi, or Phidias) and less commonly by τ (tau, which means cut in ancient Greek).
The Golden Ratio and the Fibonacci Number:
The golden ratio is based on the Fibonacci number. In Fibonacci sequence, every number, after the second one, is the sum of the previous two numbers. The ratio of a number and the number before that in Fibonacci sequence goes like:
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.666...
8/5 = 1.6
13/8 = 1.625
21/13 = 1.61538...
34/21 = 1.61905...
55/34 = 1.61764...
89/55 = 1.61861...
which would lead to 1.6180339887..., phi, or golden ratio.
The Golden Ratio
Other Names for the Golden Ratio:
Phi (φ), golden section, golden mean, extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, golden number, or mean of Phidias are the other names for the "Golden Ratio".
The Golden Ratio:
The golden ratio is the number often encountered when taking the ratios of distances in simple geometric figures, like pentagon, pentagram, decagon, and dodecahedron. If the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller quantity, then those to quantities are in the golden ratio. The golden ratio is approximately 1.6180339887... , which is similar to pi (π) because they are both irrational mathematical constant. The golden ratio can be found in almost everywhere, as in architecture, painting, book design, music, nature, mathematics, etc.
History of the Golden Ratio:
The study of the golden ratio started at least 2400 years ago by ancient Greek mathematicians because of its frequent appearance in geometry. In Elements, Euclid's book that was one of the first and influential book of golden ratio, he defined the golden ratio as: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser" Luca Pacioli, who captured golden ratio in the imaginations of artist, architects, scientist, and mystics, started the modern history of the golden ratio. It was twentieth century when the golden ratio started to be commonly represented by the Greek letter φ (phi, or Phidias) and less commonly by τ (tau, which means cut in ancient Greek).
The Golden Ratio and the Fibonacci Number:
The golden ratio is based on the Fibonacci number. In Fibonacci sequence, every number, after the second one, is the sum of the previous two numbers. The ratio of a number and the number before that in Fibonacci sequence goes like:
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.666...
8/5 = 1.6
13/8 = 1.625
21/13 = 1.61538...
34/21 = 1.61905...
55/34 = 1.61764...
89/55 = 1.61861...
which would lead to 1.6180339887..., phi, or golden ratio.
The Golden Ratio:
The golden ratio can be represented by
First, I have to find the ratio to get to this point.
Then, this goes next where a=bφ
Then, divide the equation by b and make it into an equation where I can use quadratic formula to solve.
Pictures of Golden Ratio:
Sources:
- "Golden ratio" - From Wikipedia, the free encyclopedia. 19 October 2009. <http://en.wikipedia.org/wiki/Golden_ratio>- Weisstein, Eric W. "Golden Ratio." From //MathWorld//--A Wolfram Web Resource. <http://mathworld.wolfram.com/GoldenRatio.html>
- Livio, Mario. "The golden ratio and aesthetics" 19 October 2009. <http://plus.maths.org/issue22/features/golden/index.html>
- Bourne, M. "The Math Behind the Beauty" 19 October 2009. <http://www.intmath.com/Numbers/mathOfBeauty.php>
Pictures:
- <http://nazmath.net/Online_Classes/HTML2/Wk2/goldenRatio.htm>- <http://jwilson.coe.uga.edu/EMT669/Student.Folders/Frietag.Mark/Homepage/Goldenratio/goldenratio.html>
- <http://www.highlandwoodworking.com/woodnews/july_2006/ask_the_staff_july06.html>